Choe Ryong-Hae told Xi that North Korea is willing to take positive actions to solve problems through dialogue, the semi-official China News Service said, after months of high tensions over Pyongyang's nuclear programme.
The report did not disclose the contents of the letter.
It quoted Choe saying dialogue included the long-stalled six-party talks aimed at North Korea's denuclearisation, which are chaired by China and bring together the two Koreas, the US, Russia and Japan.
China is North Korea's key economic benefactor and diplomatic protector.
The report quoted Xi as telling Choe that China's position is for the denuclearisation of the Korean peninsula and Beijing hopes for a resumption of the six-nation negotiations.
The six-party talks have sought to persuade Pyongyang to abandon nuclear development in exchange for aid and security guarantees, but the process has stalled for years amid repeated North Korean atomic tests and ballistic missile launches.